Christina Zarb

activity

20152026

most citedSelective Hypergraph Colourings

1 citations · 1 across the 5 of their papers we have counts for

collaborators

6 papers

math.CO2020

On zero-sum spanning trees and zero-sum connectivity

Yair Caro, Adriana Hansberg, Josef Lauri +1

We consider $2$ -colourings $f : E (G) \to {- 1, 1}$ of the edges of a graph $G$ with colours $- 1$ and $1$ in $Z$ . A subgraph $H$ of $G$ is said to be a zero-sum…

math.CO2019

A note on totally-omnitonal graphs

Yair Caro, Josef Lauri, Christina Zarb

Let the edges of the complete graph $K_{n}$ be coloured red or blue, and let $G$ be a graph with $∣ V (G) ∣ < n$ . Then ot(n,G) is defined to be the minimum integer, if it exists, such t…

math.CO2019

On small balanceable, strongly-balanceable and omnitonal graphs

Yair Caro, Josef Lauri, Christina Zarb

In Ramsey theory for graphs we are given a graph $G$ and we are required to find the least $n_{0}$ such that, for any $n \geq n_{0}$ , any red/blue colouring of the edges of $K_{n}$ gives…

math.CO2018

Notes on Spreads of Degrees in Graphs

Yair Caro, Josef Lauri, Christina Zarb

Perhaps the very first elementary exercise one encounters in graph theory is the result that any graph on at least two vertices must have at least two vertices with the same degree…

math.CO2015★ 1 cited

Selective Hypergraph Colourings

Yair Caro, Josef Lauri, Christina Zarb

We look at colourings of $r$ -uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$ -uniform hy…

math.CO2015

Ramsey numbers for degree monotone paths

Yair Caro, Raphael Yuster, Christina Zarb

A path $v_{1}, v_{2}, \dots, v_{m}$ in a graph $G$ is $d e g r ee$ - $m o n o t o n e$ if $d e g (v_{1}) \leq d e g (v_{2}) \leq \dots \leq d e g (v_{m})$ where $d e g (v_{i})$ is the degree of $v_{i}$ in $G$ . Longest degr…